The Acme Pie Company received an initial advance of $9,900 on its operating line on June 3rd. The simple interest rate on the account was initially 5.88% and increased to 6.05% on June 20th. How much interest was owing on the account at the end of the month (June 30th)? Round your answer to two decimal places, but don't include the $ sign.
To find the amount of interest owing on the account at the end of June, we need to calculate the interest for the period between June 3rd and June 30th.
First, let's calculate the interest for the period from June 3rd to June 20th using the initial interest rate of 5.88%.
Step 1: Calculate the number of days between June 3rd and June 20th.
There are 17 days between these two dates.
Step 2: Calculate the interest for the period using the formula:
Interest = Principal * Rate * Time
Interest = $9,900 * 0.0588 * (17 / 365)
Note: We divide the number of days by 365 to get the time in years.
Calculating this, we get:
Interest = $9,900 * 0.0588 * (17 / 365) = $84.57
Therefore, the interest owed between June 3rd and June 20th is $84.57.
Now, let's calculate the interest for the period from June 20th to June 30th using the increased interest rate of 6.05%.
Step 1: Calculate the number of days between June 20th and June 30th.
There are 10 days between these two dates.
Step 2: Calculate the interest for the period using the formula:
Interest = Principal * Rate * Time
Interest = $9,900 * 0.0605 * (10 / 365)
Calculating this, we get:
Interest = $9,900 * 0.0605 * (10 / 365) = $51.01
Therefore, the interest owed between June 20th and June 30th is $51.01.
Finally, let's calculate the total interest owed for the entire month of June.
Total Interest = Interest from June 3rd to June 20th + Interest from June 20th to June 30th
Total Interest = $84.57 + $51.01 = $135.58
Therefore, the interest owing on the account at the end of June 30th is $135.58.